Skew cyclic codes over ${\mathbb{F}}_q+v{\mathbb{F}}_q+v^2{\mathbb{F}}_q$

Abstract

In this article, we study skew cyclic codes over ring $R={\mathbb{F}}_q+v{\mathbb{F}}_q+v^2{\mathbb{F}}_q$, where $q=p^m$, $p$ is an odd prime and $v^3=v$. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over $R$ by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent generators of skew cyclic codes over ${\mathbb{F}}_q$ and $R$ are considered.

This manuscript has been accepted by a magazine. arXiv admin note: text overlap with arXiv:1504.07831